Question: Solve for $x$ and $y$ using elimination. ${4x+3y = 51}$ ${5x-3y = 30}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $3y$ and $-3y$ cancel out. $9x = 81$ $\dfrac{9x}{{9}} = \dfrac{81}{{9}}$ ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {4x+3y = 51}\thinspace$ to find $y$ ${4}{(9)}{ + 3y = 51}$ $36+3y = 51$ $36{-36} + 3y = 51{-36}$ $3y = 15$ $\dfrac{3y}{{3}} = \dfrac{15}{{3}}$ ${y = 5}$ You can also plug ${x = 9}$ into $\thinspace {5x-3y = 30}\thinspace$ and get the same answer for $y$ : ${5}{(9)}{ - 3y = 30}$ ${y = 5}$